Leicester boss Levein held the edge in Edinburgh when he was manager of Hearts and Plymouth manager Williamson was in charge of Hibernian, and the pattern has continued south of the border.
Chasing the double over Plymouth after a 2-1 win back in November, Leicester never really threatened to make it two wins in a row.
However, their defence largely managed to hold the home team comfortably at bay and, when the Pilgrims did get behind them, the woodwork came to the visitors rescue.
Scott Taylor hit the post after latching on to a long, low, pass to the front, pushing past Darren Kenton and driving the ball across Canadian international goalkeeper Lars Hirschfeld.
The unlucky Taylor hit the post again in time added on at the end of the first half. From Nick Chadwick's short pass, he dummied round Alan Sheehan before firing in a shot which Hirschfeld touched on to the woodwork.
Leicester did have the ball in the net, early in the second half when Icelandic international Joey Gudjonsson - who was playing against his brother Bjarni for the first time at senior level - fired home, but the effort was ruled out for offside.
Argyle defender David Worrell was substituted 13 minutes from the end of the game and received a standing ovation, but his replacement, Luke Summerfield, the son of former Argyle player and now Sheffield Wednesday coach Kevin Summerfield, could not produce a dream end to the season.